The Acme Insurance company has two types of customers, careful and reckless. A careful customer has an accident during the year
with a probability of 0.01. A reckless customer has an accident during the year with a probability of 0.04. 80% of the customers are careful and 20% of the customers are reckless. Suppose a randomly chosen customer has an accident this year. What is the probability that this customer is one of the careful customers
Answer:The total probability that a random person has an accident in the given year is
.8×.01+.2×.04=0.016
The portion of that which is explained by careful drivers is .8×.01=.08. Thus the answer is
.8×.01.8×.01+.2×.04=.5
Thus it is equally likely that your accident victim was careful or careless.
Speaking informally, that's because, while it's four times more likely that a randomly selected driver is careful, it is one fourth as likely that a careful driver will have an accident, and the two
